Counterpoint
(Keep in mind that the point in learning counterpoint is not to teach you how to write in a 17th century style, which is a common misconception. If you read the works of Heinrich Schenker, you'll find that a lot of the greatest classical works when simplified using Schenker's techniques read as perfect species counterpoint. Studying strict counterpoint and doing the exercises naturally strengthens your ability to write with good voice leading in your free compositions wherever you feel it's necessary.)

If you're reading this, I assume you're interested in becoming a composer. My advice to you is this; Don't. Unless you can't live without music, unless you feel that there's absolutely nothing else in the world you'd rather do, unless you need several hours of your favorite composer/artist every day simply to live, just don't bother.

Composition is a very unrewarding, very difficult, very lonely, and often very unfulfilling line of work. If you wish to become a composer, you are in for years and years of unavoidably tortuous, monotonous, soul-crushing mental training, failed compositions, feelings of inadequacy, utter indifference to your work (even from your closest friends), and after all of this, there is still absolutely no guarantee of success. 99.9% of people in this field die unfulfilled in obscurity.

Are you still willing to go through with this?

Go to the keyboard now and improvise a fugue in the style of Bach on whatever theme you like. Can't do that? Go to the keyboard and play a whole tone scale in the bass starting on E-flat, and harmonize it in the treble with minor seventh chords (according to the rules of voice leading, of course), and we'll see what it sounds like. No? Go to the keyboard and play the first prelude of Bach's Well Tempered Clavier transposed to A-flat major. Can you not do that? If I play you an aria from a Mozart opera, will you be able to transcribe it after one hearing? No? Can you realize a simple figured bass? Can you even play a C major scale with the proper fingering? Do you even have a keyboard?

You might think that some of this sounds very unnecessary and that I'm expecting you to perform miracles, but unfortunately these sorts of things are the minimum that's expected of you. To be effective as a musician and a composer, music should be as fluent to you as language is to everyone else. Would you not expect an author to do the equivalent of these things with language? Most people think of these things as something only a genius or a very talented person can do (and of course we don't mind that), but in reality, it should be perceived as basic competence.

Do you still want to become a composer? If you do, read on, and don't make too many plans for the rest of your life. Good luck...

I'd recommend at minimum dedicating at least 15 to 30 minutes to this every day (at most an hour or two). Get yourself into a schedule that you can keep up for the next few years, and be sure to continue composing outside of your education.

Start out with these to get your feet wet, and to become familiar and comfortable with how music is discussed:

Now the real fun begins. You need to start by training your ears (you should be able to identify types of chords by sight/ear, identify pitches by sight/ear, keys etc. etc.) and becoming competent at playing the keyboard. With regards to playing the keyboard, there's really no way around this. You can try training yourself on something like the guitar (as Berlioz and many popular musicians did) if you really want to, but you're sort of shooting yourself in the foot. Buy a cheap MIDI controller and plug it into FL studio and you're off. (The MIDI controller I use is an Oxygen 88, if you're interested). If you're questioning whether or not you need to be able to play at all, imagine an author who's unable to speak.

The goal here is not to train you to write in the style of Palestrina (though that is a side effect), it is rather to train your subconscious mind to treat each line as an independent living voice, and in order to get each voice to interact in such a way that the music is always pure and interesting to the ears. Music written with this foundation will flow through the listener's mind with ease and fluency. It is a strong, invisible and transparent foundation upon which you can express yourself with absolute fluency no matter what style you're writing in, and it's been this way (in the Western world) for the past 500 years.

In addition to studying counterpoint, you must also study harmony. The tried and true method is by learning how to realize figured basses (at sight on the keyboard, and on paper in both open and closed score, which you can do in the Counterpointer software), which JS Bach himself explains here: http://normanschmidt.net/scores/bachjs-general_bass_rules.pdf

In addition to all of this, the rest of your life should be dedicated to studying the music of other composers (it really doesn't matter who), and figuring out what makes their music tick, and how you can use their tricks in your own music. I can't really be too specific on how to go about this, but I have some recommendations on where to start so that you can begin to learn how to analyse music yourself:

Use whatever academic resources you can get your hands on, absorb any lectures you find. Read every biography on your favorite composers and figure out their methods of working. Join classical music forums and mailing lists and discuss the issues facing music today with your peers.

Nadia Boulanger was a music theory teacher in the twentieth century, who is known for teaching a huge number of recognizable names in music, including; Aaron Copland, Philip Glass, Daniel Barenboim. She was also close friends with composers such as Leonard Bernstein and Igor Stravinsky, who would often present new works to her for her feedback.

This is awesome. I've just messed around a bit with harmony after downloading and reading the book by Tchaikovsky, and just knowing a bit about harmonic thirds and sixths... it's revolutioned my writing already! I can't believe you don't have dozens of positive comments already on such an useful resource collection.

This is awesome. I've just messed around a bit with harmony after downloading and reading the book by Tchaikovsky, and just knowing a bit about harmonic thirds and sixths... it's revolutioned my writing already! I can't believe you don't have dozens of positive comments already on such an useful resource collection.

Holy bump-age. But thank you, I'm glad you're finding it useful.

I really need to update this (if only I had more time). My views on music education have changed a bit in the past two years.